Study on chain structure model of evolutionary game based on symmetric case

In order to overcome the limitation that traditional evolutionary game model could not compute results of one-shot game or short-term economic equilibrium etc., the paper designs a chain structure model of evolutionary game based on the symmetric income situation. Furthermore, we discover deeply that individuals in the game are in correlative dependence and in conversion with each other, and also we establish transfer relation between individual quantity of each population and expected average payments of interrelated parts in per-step of the game. On the basis of these, taking one symmetric hawk-dove game as an example, we imitate and analyze its replication dynamics and evolutionary stable strategy (ESS). The imitation showed that there just exists unique equilibrium (x) decided by ESS in the hawk-dove game. And the left region is the replication and evolution zone of hawk, where the quantity of hawk grows and that of dove goes down; the right region of x is the replication and evolution zone of dove where number of dove increases and that of hawk decrease.